107 citations · 250 across the 39 of their papers we have counts for
32 papers · 1 filter
A duality approach to the fractional Laplacian with measure data
Kenneth H. Karlsen, Francesco Petitta, Suleyman Ulusoy
We describe a duality method to prove both existence and uniqueness of solutions to nonlocal problems like with vanishing condition…
Stochastic electromechanical bidomain model
Mostafa Bendahmane, Kenneth H. Karlsen, Fatima Mroue
We analyze a system of nonlinear stochastic partial differential equations (SPDEs) of mixed elliptic-parabolic type that models the propagation of electric signals and their effect…
A nonlocal Lagrangian traffic flow model and the zero-filter limit
Giuseppe M. Coclite, Kenneth H. Karlsen, Nils Henrik Risebro
In this study, we start from a Follow-the-Leaders model for traffic flow that is based on a weighted harmonic mean (in Lagrangian coordinates) of the downstream car density. This r…
Quantitative compactness estimates for stochastic conservation laws
Kenneth H. Karlsen
We present a quantitative compensated compactness estimate for stochastic conservation laws, which generalises a previous result of Golse & Perthame (2013) for deterministic equati…
Global existence of dissipative solutions to the Camassa--Holm equation with transport noise
Luca Galimberti, Helge Holden, Kenneth H. Karlsen +1
We consider a nonlinear stochastic partial differential equation (SPDE) that takes the form of the Camassa--Holm equation perturbed by a convective, position-dependent, noise term.…
Global well-posedness of the viscous Camassa--Holm equation with gradient noise
Helge Holden, Kenneth H. Karlsen, Peter H. C. Pang
We analyse a nonlinear stochastic partial differential equation that corresponds to a viscous shallow water equation (of the Camassa--Holm type) perturbed by a convective, position…